Design And Analysis Of Experiments Lecture Notes

Design And Analysis Of Experiments Lecture Notes – Course objectives and concepts A brief history of DOE Experimental design Some basic terms and terminology Guidelines for planning, conducting and analyzing experiments D. Arku DOE Course 2

First course in STAT306 heard about normal distribution know about mean and variance have done regression analysis or heard about it know about ANOVA or heard about it Have knowledge of using SPSS Not yet heard about fractional, factorial design etc. Arku DOE 3 courses

Design And Analysis Of Experiments Lecture Notes

Sir Ronald A. Fisher – the pioneer invented ANOVA and applied statistics to experimental design while working at the Agricultural Experiment Station in Rothamsted, London, England. George E. P. Box – married Fisher’s daughter while still working (86 years old) developed the reaction method (1951) and many other contributions to s44tatistics Among others Raymond Myers, J. S. Hunter, WG Hunter, Yates, Montgomery, Finney, etc.. DOE Course 4

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R. A. Fisher and his colleagues Great influence of agricultural science on Factorial design, ANOVA The first industrial era, 1951 – late 1970s Box and Wilson, refuge Application of industrial and chemical processes The second industrial era, after the 1970s – 1990s to improve the quality of the effort. in many companies Taguchi and stable parameter design, system stability Current period, starting around 1990 General use of computer technology in DOE Increased use of DOE in Six-Sigma and in business Use of DOE in computer tests D. Arku DOE Course 5

6 References D. G. Montgomery (2008): Design and Analysis of Experiments, 7th Edition, John Wiley and Sons is one of the best books on the market. Uses Professional Design software for graphics. You use letters in Factors. G. E. P. Box, W. G. Hunter, and J. S. Hunter (2005): Statistics for Surveyors: An Introduction to Design, Data Analysis, and Model Construction, John Wiley and Sons. 2nd Edition A standard text with many examples. There are no computer-aided solutions. You use numbers in Factors. Journal of Quality Technology, Technometrics, American Statistician, special journals in D. Arku Course DOE 6

Experiment – an experiment or series of experiments in which purposeful changes are made to input variables or process elements in order to observe and identify the causes of changes in output response. Question: 5 factors, and 2 response variables You want to know the effect of each factor on the response and how the factors interact. answers – e.g. increase Y1 but decrease Y2 Time and budget set for only 30 test runs. DOE Course 7

The best estimation method (trial and error) can go on forever and does not guarantee to find a solution. A factor-at-a-time method is inefficient (requires many runs of the experiment) and failed to consider any possible interaction between the factors. ) Different factors and the right, current, and most effective method Can ensure how things work together. DOE 8 Courses

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2-level full factorial (2k) fractional factorial (2k-p), and response space method (RSM) All DOEs are based on the same statistical principles and analysis methods – ANOVA and recovery analysis. DOE 9 Course

All experiments must be designed experiments Unfortunately, some experiments are poorly designed – valuable resources are used inappropriately and the results are inconclusive. DOE 10 courses

DOE allows experiments to develop a mathematical model that predicts how input variables interact to produce output variables or responses to a process or system. DOE can be used for a wide range of tests for various purposes including almost all areas of engineering and business marketing. DOE Course 11

Learn about the process we are analyzing Screen important variables Create a mathematical model Find the predictive equation Prepare an answer (if necessary) Statistical significance is tested using ANOVA, and a predictive model can be seen using regression analysis. DOE 12 course

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Experiments are conducted in the field of engineering to: test and compare basic design configurations to test different devices select design parameters so that the design works well under a wide range of conditions field (robust design) to identify key design parameters that affect performance DOE Course 13.

1. Identifying the objectives in the form of specific questions and design structure 2. Selecting the treatment to provide answers to the questions 3. Selecting the experimental unit and replication size 4. Managing the difference between sets of units by using blocking methods or by using auxiliary information (ie covariate information) collected from units 5 Allocation of treatment to specific units (randomization) DOE Course 14

6. Collect data related to the research objectives 7. This may be for the entire assessment unit or may include a sample within the unit 8. Statistical analysis of the collected data DOE Course 15

17 PHASE PHASE Let’s define the terms of treatment, factor and level by considering Experiment to test 24 varieties of cowpea Experiment to test 8 varieties under three different levels of fertility. Course 17

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The first experiment has a factor category with 24 levels (treatment and treatment levels are not different from the second, there are two factors, different from 8 levels and fertility 3 levels (24 different combinations / treatments) the third three factors of level 4 , 3 and 2 each Includes 24 treatments Course DOE 18

19 VOCABULARY Units of assessment are the things we use in treatment, e.g. plots of land, customer groups and more. The treatments are different programs that we want to compare. E.g. Different types or amounts of fertilizer, etc. Experimental Error is the random variation present in all test results; Different test units will give different responses to the same treatment. Or applying the same treatment repeatedly to the same unit may cause different responses. It’s not a bad attempt. Things combine to make a cure. The settings for each item are called DOE Course 19 levels

20 GLOSSARY Confounding – occurs when the effect of one cause or treatment cannot be distinguished from another cause or treatment. Two issues or treatments are said to be confused. E.g. Consider planting grade A maize in GT and grade B in Cape Coast. In this case we cannot separate the local effects from the different effects. A variety of factors and local conditions confound DOE’s Course 20

Photo factors: film speed, light, shutter speed Answer: quality of slides made near flash attachment Boiling water Factors: Type of pan, size of burner, lid Answer: Time to boil water D-day factors: Type of drink, amount of drink. Drinks, rate of drinking, time after last meal Answer: Time to find a metal ball in the maze.

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Factors: amount of wine, oyster sauce, sesame oil Answer: The taste of grilled chicken Basketball Factors: Distance from the basket, type of shot, floor area Answer: Number of shots made (out of 10) in basketball , temperature, type of wax Answer: Time to go to the ski slope DOE Course 22

The process of designing an experiment so that relevant data can be analyzed using statistical methods that lead to valid, objective, and meaningful conclusions from the data involves two aspects: design and statistical analysis of the DOE Course 23

Hypothesis – a hypothesis that motivates an experiment Experiment – an experiment conducted to investigate a hypothesis Analysis – a statistical analysis of data from an experiment Conclusion – what was learned about original hypothesis from experiment. DOE 24 courses

Replication allows estimation of experimental error allows more accurate estimation of sample base value Randomization cornerstone of all statistical methods “averaging” results outliers reduces bias and systematic errors. Course 25

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Researchers use experiments to answer a question. Common questions are Is the drug a safe, effective treatment for the disease? This could be a test of how AZT affects the development of AIDS What combination of protein and carbohydrate sources provides the best nutrition for growing sheep under what conditions should I use the my chemical cleaner given the grade of raw material this month? DOE Course 26

Will short prison terms for partner abusers prevent future attacks How mobile network usage will change if our company offers a different level to our customers DOE Course 27

It allows us to establish a direct comparison between the treatments of interest We design the experiment to reduce any comparison bias or to reduce comparison error Above all, we control the experiments and allow us to make strong on inferences about the nature of the experiment. the difference we see in the test. In particular, we can speculate on the cause of the DOE 28 course

29 Why Should You Taste? Mosteller and Turkey (1997) list three

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